Question

Find the percentage increase in the area of a triangle if its each side is doubled.​

Answer 1

Step-by-step explanation:

Semi-perimeter of the triangle, s=

2

a+b+c

Area of triangle =

s(s−a)(s−b)(s−c)

.

When each side is doubled, the new sides are 2a,2b,2c.

Hence, new s

′

=

2

2a+2b+2c

=2(

2

a+b+c

)=2s

New area A

′

=

2s(2s−2a)(2s−2b)(2s−2c)

=

2×2×2×2×s(s−a)(s−b)(s−c)

=4

s(s−a)(s−b)(s−c)

.

∴ % change in Area =

A

A

′

−A

×100

=

s(s−a)(s−b)(s−c)

4

s(s−a)(s−b)(s−c)

−

s(s−a)(s−b)(s−c)

×100

=

1

4−1

×100

=300%